Most power output systems are designed to operate at relatively constant voltage because this is typical of the discharge characteristics of most battery chemistries. In comparison to battery chemistries, state of the art ultracapacitor devices store less energy per volume and weight. Also, ultracapacitor discharge curves are significantly different than battery discharge curves. Battery discharge curves are relatively flat as most of the energy is dissipated from the devices. Most systems are designed to operate in this relatively flat portion of the curve. Ultracapacitors, on the other hand, do not have a flat voltage region. Instead, the voltage varies approximately linearly with a constant current discharge.
Ultracapacitors are commonly viewed or modeled as an ideal capacitor. In fact, the device is considerably more complex. However, for the purposes of this discussion the ideal capacitor model will be used. Equation 1 describes the relationship between voltage, current, and capacitance of an ideal ultracapacitor.
                              i          ⁡                      (            t            )                          =                  C          ⁢                                    ⅆ              v                                      ⅆ              t                                                          (                  Equation          ⁢                                          ⁢          1                )            
From this equation it is known that for a constant discharge current, the voltage of an ultracapacitor varies linearly with a slope of dv/dt being equal in magnitude to l(t)/C. Also, the amount of stored energy that can be used from an ultracapacitor is dependant on the amount of voltage swing a system can allow. For an ultracapacitor with a given capacitance C, and an allowable voltage swing from Vhigh to Vlow the amount of usable energy can be calculated from Equation 2.
                              E          uc                =                              1            2                    ⁢                      C            ⁡                          (                                                V                  high                  2                                -                                  V                  low                  2                                            )                                                          (                  Equation          ⁢                                          ⁢          2                )            
From Equation 2, it is clear that the larger the allowable voltage swing of an ultracapacitor cell, the larger the amount of stored energy that can be utilized. Therefore, a system that best utilizes the energy storage capabilities of an ultracapacitor is a system that can allow for the largest voltage swing possible.
Primary and secondary battery powered systems can also benefit from systems that allow for a large voltage swing. However, because a smaller percentage of a battery's usable energy is utilized by a wide voltage swing, the gain is less significant with a battery than it is with an ultracapacitor.
Recently, white and color LED technology has improved significantly. The color quality, efficacy, and total light output per device continue to improve. Because of these recent advancements LEDs are being used more frequently in consumer and commercial applications.
LEDs exhibit a nonlinear voltage to current relationship and the voltage for a given current will vary slightly from device to device. The amount of light emitted from an LED at a given temperature is based on current. Therefore, in order to achieve a consistent and predictable light output it is best to drive the LED with a constant current.
Currently there exist many methods of driving LEDs. Many of these circuits drive LEDs with a constant current, but the current regulation is poor and therefore the light output varies as the input voltage to the circuit goes down. The input voltage of ultracapacitors and batteries go down during discharge. Furthermore, existing circuits have a limited input voltage range in comparison to the disclosed technology. And over this limited range the efficiency may be very low. For ultracapacitor systems, the efficiency is critical because the energy density is typically lower for state of the art ultracapacitors vs. state of the art batteries. However, efficiency is still important for battery-powered systems as well as other sources of electrical power.
Digital controllers can provide unique functionality to consumer products. In the case of hand-held lighting the use of a digital controller can provide, for example, unique light output profiles based on input voltage, unique types of user interface and unique flash patterns. State of charge and other calculations can easily be performed. Digital controllers can also operate down to very low voltages, which make them advantageous in control systems over alternative methods.